Risk Management and Investment Management is a key FRM Part 2 topic worth 15% of the exam. This guide covers the essential concepts.

Modern Portfolio Theory (MPT)

Key Principles

  • Investors are risk-averse (prefer less risk for the same return)
  • Diversification reduces risk (for imperfectly correlated assets)
  • The efficient frontier represents optimal risk-return portfolios
  • The risk-free asset enables the Capital Market Line (CML)

Portfolio Risk

For a two-asset portfolio: σ²_p = w²₁σ²₁ + w²₂σ²₂ + 2w₁w₂σ₁σ₂ρ₁₂

Diversification benefit depends on correlation (ρ):

  • ρ = 1: No diversification benefit
  • ρ < 1: Portfolio risk < weighted average of individual risks
  • ρ = -1: Perfect diversification possible

Capital Asset Pricing Model (CAPM)

E(Rᵢ) = Rf + βᵢ[E(Rm) - Rf]

  • Only systematic risk (β) is priced
  • β = Cov(Rᵢ, Rm) / Var(Rm)
  • The Security Market Line (SML) shows the expected return for each β

Multi-Factor Models

Fama-French Three-Factor

E(R) = Rf + β₁(Rm-Rf) + β₂(SMB) + β₃(HML)

  • Market, Size, and Value factors

Carhart Four-Factor

Adds Momentum (WML — Winners Minus Losers) to Fama-French

Five-Factor (Fama-French)

Adds Profitability (RMW) and Investment (CMA) factors

Performance Measurement

Risk-Adjusted Measures

  • Sharpe Ratio: (Rp - Rf) / σp — return per unit of total risk
  • Treynor Ratio: (Rp - Rf) / βp — return per unit of systematic risk
  • Information Ratio: α / TE — alpha per unit of active risk
  • Sortino Ratio: (Rp - T) / σ_downside — return per unit of downside risk

Performance Attribution

Decomposing returns into:

  • Allocation Effect: Being in the right sectors
  • Selection Effect: Picking the right securities
  • Interaction Effect: Combined impact

Risk Budgeting

Allocating risk across the portfolio:

  • Define total risk budget (tracking error budget, VaR budget)
  • Allocate to strategies/managers
  • Monitor marginal risk contributions
  • Rebalance to maintain risk allocation

Hedge Fund Risk

Unique challenges:

  • Leverage: Amplifies gains and losses
  • Illiquidity: Lock-up periods, hard-to-value positions
  • Tail Risk: Strategies may have non-normal return distributions
  • Operational Risk: Less regulated, less infrastructure
  • Survivorship Bias: Performance data skewed by failed funds

Prepare for investment risk questions with our comprehensive practice bank!